In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.57

7.57 Drive-thru customer service.

QSRMagazine.com assessed 1855 drive-thru visits at quickservice restaurants.28 One benchmark assessed was customer service. Responses ranged from “Rude (1)” to “Very Friendly (5).” The following table breaks down the responses according to two of the chains studied.

drvthru

Rating
Chain 1 2 3 4 5
Taco Bell 0 5 41 143 119
McDonald’s 1 22 55 139 100
  1. A researcher decides to compare the average rating of McDonald’s and Taco Bell. Comment on the appropriateness of using the average rating for these data.
  2. Assuming an average of these ratings makes sense, comment on the use of the procedures for these data.
  3. Report the means and standard deviations of the ratings for each chain separately.
  4. Test whether the two chains, on average, have the same customer satisfaction. Use a two-sided alternative hypothesis and a significance level of 5%.

7.57

(a) The problem with averages on rating is that there is no guarantee the differences between ratings are equal, so that going from a rating of 1 to 2, and 2 to 3, etc., are equal. Taking averages assumes this so it is likely not appropriate. (b) The data are ratings from 1–5; as such they certainly will not be Normally distributed but because and outliers are not possible, the procedures can be used. (c) McDonald’s: . Taco Bell: . (d) . The data are significant at the 5% level, and there is evidence the average customer ratings between the two chains is different.